Adelic models of tensor-triangulated categories
Algebraic Topology
2020-07-28 v3 Commutative Algebra
Category Theory
Abstract
We show that a well behaved Noetherian, finite dimensional, stable, monoidal model category is equivalent to a model built from categories of modules over completed rings in an adelic fashion. For abelian groups this is based on the Hasse square, for chromatic homotopy theory this is based on the chromatic fracture square, and for rational torus-equivariant homotopy theory this is the model of Greenlees-Shipley arXiv:1101.2511.
Cite
@article{arxiv.1903.02669,
title = {Adelic models of tensor-triangulated categories},
author = {J. P. C. Greenlees and Scott Balchin},
journal= {arXiv preprint arXiv:1903.02669},
year = {2020}
}
Comments
Hypotheses weakened and simplified. Polished. To appear in Advances in Mathematics